i have also no oil cooler in my astra g with z22se s/c and cr around 9,0 : 1
max oil themp. is 125 , measured at oil filter. but no race track.
with good oil it´s no problem.
the only gain with an water to oil cooler is heating oil after cold start.
ok, or cooling if biggest race track.
astra g has engine in the front, with much air comming to the engine.
vx 220 has engine at back. more problems with themp. so, they have an oil cooler.
it´s a water to oil cooler. that means, if engine is cold the oil cooler heats the oil. so the engingine is quickly on oil themp.
it´s good for engine, not so much wear after coold start.
if oil get more then around 90- 95 the oil cooler cool down the oil.
hope your ecu remap ist fine. enjoy the s/c